French billionaire François Pinault popped into the London headquarters of auction house Christie’s one day in 1994 to see some art. He was accompanied by one of his employees, Patricia Barbizet, who helped translate, recalls Brett Gorvy, the Christie’s expert who greeted them.

Last week, Mr. Pinault stunned the art world by promoting Ms. Barbizet to chief executive of Christie’s, which he bought in 1998. “I had no idea how far she’d go,” says Mr. Gorvy, now Christie’s chairman and international head of postwar and contemporary...